(a) The State Fiscal Accountability Authority, or the political subdivision where it has not purchased insurance from the State Fiscal Accountability Authority, may adjust, compromise, settle, or allow any claim or settle or compromise any action.

(b) Whether or not the claim is filed, the claimant is entitled to institute an action against the appropriate agency or political subdivision. Provided, however, if a claimant files a claim, he may not institute an action until after the occurrence of the earliest of one of the following three events: (1) the passage of one hundred eighty days from the filing of the claim with the governmental entity, (2) the governmental entity’s disallowance of the claim, or (3) the governmental entity’s rejection of a settlement offer.